Unimodality of steady state distributions of growing cell populations

We consider an equation for the evolution of growing and dividing cells, and show, using a result of Kato and McLeod, that the probability density function for the stationary size distribution is necessarily unimodal

Determinação gráfica da parábola conhecidos dois pontos da curva e a tangente no vértice (exemplo prático de geometria aplicada ao design)

No âmbito da geometria euclidiana, abordada do ponto de vista gráfico, propõe-se um procedimento para obter a parábola, conhecidos dois pontos desta e a tangente no vértice. Os dois pontos podem estar a iguais ou a diferentes distâncias da tangente no vértice. Este problema tem solução através de uma construção incomum (Fig. 1), que divulgámos anteriormente em BONIFÁCIO, 2005, 64, e que consiste em determinar o ponto médio M entre a projecção ortogonal de um ponto P da parábola na tangente do vértice e o próprio vértice. PM é a tangente em P. A perpendicular à tangente em M intersecta o eixo da parábola no foco. É feita também aplicação do conceito que define que, do ponto de vista gráfico, as parábolas são todas semelhantes, assumindo tamanhos diferentes ao variar a distância focal. São utilizados conjuntamente métodos da geometria plana e da geometria descritiva

Uma tipografia de base elíptica e outros cruzamentos do design com a geometria das curvas cónicas

Através de alguns exemplos práticos, pretende-se defender que o conhecimento geométrico e, em particular, o conhecimento das curvas cónicas e suas aplicações, pode potenciar o trabalho projetual dos designers, diminuir os custos de hardware e software no ensino e no trabalho profissional, diminuir a necessidade de recurso a meios sofisticados e caros, reduzir a necessidade de permanente atualização dos meios tecnológicos, e de utilização de software que implique formação especializada e, sobretudo, que necessite de longos períodos de formação. Temos em vista contribuir para o reconhecimento da importância do estudo destas curvas e das superfícies por elas geradas, em especial no ensino da Geometria em cursos de Design. De facto, a partir da sistematização do conhecimento existente em outras áreas, como, por exemplo, a arquitetura e as engenharias, pelo aprofundamento da adaptação de propriedades das cónicas e de conhecimentos de áreas, como a geometria analítica ou a projetiva para a linguagem dos traçados geométricos, e pela contribuição com a sugestão de novos traçados, pode desenvolver-se a capacidade dos designers e estudantes de design resolverem problemas, no âmbito do projeto, na representação técnica e na comunicação externa com não peritos

Population expansion in the North African Late Pleistocene signalled by mitochondrial DNA haplogroup U6

Background <br/> The archaeology of North Africa remains enigmatic, with questions of population continuity versus discontinuity taking centre-stage. Debates have focused on population transitions between the bearers of the Middle Palaeolithic Aterian industry and the later Upper Palaeolithic populations of the Maghreb, as well as between the late Pleistocene and Holocene. <br/> Results Improved resolution of the mitochondrial DNA (mtDNA) haplogroup U6 phylogeny, by the screening of 39 new complete sequences, has enabled us to infer a signal of moderate population expansion using Bayesian coalescent methods. To ascertain the time for this expansion, we applied both a mutation rate accounting for purifying selection and one with an internal calibration based on four approximate archaeological dates: the settlement of the Canary Islands, the settlement of Sardinia and its internal population re-expansion, and the split between haplogroups U5 and U6 around the time of the first modern human settlement of the Near East. <br/> Conclusions <br/> A Bayesian skyline plot placed the main expansion in the time frame of the Late Pleistocene, around 20 ka, and spatial smoothing techniques suggested that the most probable geographic region for this demographic event was to the west of North Africa. A comparison with U6's European sister clade, U5, revealed a stronger population expansion at around this time in Europe. Also in contrast with U5, a weak signal of a recent population expansion in the last 5,000 years was observed in North Africa, pointing to a moderate impact of the late Neolithic on the local population size of the southern Mediterranean coast

Closed Contour Fractal Dimension Estimation by the Fourier Transform

This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, it is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e. g., Bouligand-Minkowski, box-couting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique

Repercussions of growth path on carcass characteristics, meat colour and shear force in Alentejana bulls

The aim of this study was to evaluate the carcass and meat characteristics of eight muscles from bulls with distinct growth paths. A total of 40 Alentejana male calves were allocated to two distinct feeding regimes. In the continuous growth (CG) system, the animals were fed concentrates plus hay and were slaughtered at 18 months of age. On the other hand, in the discontinuous growth (DG) system, the animals were fed hay until 15 months of age; the cattle were then fed the same diet provided to the CG group from 15 to 24 months of age. The DG reduced hot carcass weight, fatness and dressing %, but the proportions of fat, bone and muscle tissues in the leg were not affected. In contrast, there was a positive impact of compensatory growth on supraspinatus, triceps brachii, semitendinosus, biceps femoris muscle tenderness, overcoming the negative effects of age at slaughter. The reasons for such improvement in meat tenderness were not related to intra-muscular fat content or myofibrillar protein degradation values. An association between tenderness and muscle collagen properties was not established. The results indicate that the compensatory growth has a muscle-dependent effect

A concentration phenomenon for semilinear elliptic equations

For a domain \Omega\subset\dR^N we consider the equation -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $\Omega$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in\Omega$ as $n\to\infty$. We show that if $u_n$ is a nontrivial solution corresponding to $Q_n$, then the sequence $(u_n)$ concentrates at $x_0$ with respect to the $H^1$ and certain $L^q$-norms. We also show that if the sets $\{Q_n>0\}$ shrink to two points and $u_n$ are ground state solutions, then they concentrate at one of these points

Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?

We revisit the recently found equivalence for the response of a static scalar source interacting with a {\em massless} Klein-Gordon field when the source is (i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the Hawking radiation and (ii) uniformly accelerated in Minkowski spacetime, in the inertial vacuum, provided that the source's proper acceleration is the same in both cases. It is shown that this equivalence is broken when the massless Klein-Gordon field is replaced by a {\em massive} one.Comment: 4 pages, 2 figure

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio